LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
C = 47 nFL = 2.2 mH

An ideal LC circuit has L = 2.2 mH and C = 47 nF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 mHC = 47 nF
f0 = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 5 VC = 4.7 nF

A 4.7 nF capacitor is charged to 5 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in nJ.

C = 4.7 nFV0 = 5 VL = 1 mH
W = nJ
3.Medium
C = 470 nF+−6 VL = 100 µHiL​

A 470 nF capacitor charged to 15 V oscillates with an ideal 100 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 6 V, in µJ.

C = 470 nFV0 = 15 VvC = 6 V
WL = µJ
4.Medium
V47 Ω1 mH470 pF

A series RLC circuit has R = 47 Ω, L = 1 mH and C = 470 pF. Find its bandwidth BW in kHz.

R = 47 ΩL = 1 mHC = 470 pF
BW = kHz
5.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 20 kHz and a bandwidth of 800 Hz. Find the capacitance C in nF.

R = 5 Ωf0 = 20 kHzBW = 800 Hz
C = nF
6.Hard
VR = ?4.7 mHC

A series resonant circuit uses a 4.7 mH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 4.7 mHBW = 50 kHz
R = Ω

Answer key

  1. 1. f0 = 15.65 kHz
  2. 2. W = 58.75 nJ
  3. 3. WL = 44.42 µJ
  4. 4. BW = 7.48 kHz
  5. 5. C = 63.66 nF
  6. 6. R = 1477 Ω

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